Tempo http://journals.cambridge.org/TEM Additional services for Tempo: Email alerts: Click here Subscriptions: Click here Commercial reprints: Click here Terms of use : Click here ON HORATIU RADULESCU'S FIFTH STRING QUARTET (‘BEFORE THE UNIVERSE WAS BORN’) OP. 89 William Dougherty Tempo / Volume 68 / Issue 268 / April 2014, pp 34 - 45 DOI: 10.1017/S0040298213001666, Published online: 20 March 2014 Link to this article: http://journals.cambridge.org/abstract_S0040298213001666 How to cite this article: William Dougherty (2014). ON HORATIU RADULESCU'S FIFTH STRING QUARTET (‘BEFORE THE UNIVERSE WAS BORN’) OP. 89 . Tempo, 68, pp 34-45 doi:10.1017/S0040298213001666 Request Permissions : Click here Downloaded from http://journals.cambridge.org/TEM, IP address: on 21 Mar 2014


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Additional services for Tempo:

Email alerts: Click hereSubscriptions: Click hereCommercial reprints: Click hereTerms of use : Click here


William Dougherty

Tempo / Volume 68 / Issue 268 / April 2014, pp 34 - 45DOI: 10.1017/S0040298213001666, Published online: 20 March 2014

Link to this article: http://journals.cambridge.org/abstract_S0040298213001666

How to cite this article:William Dougherty (2014). ON HORATIU RADULESCU'S FIFTH STRING QUARTET (‘BEFORETHE UNIVERSE WAS BORN’) OP. 89 . Tempo, 68, pp 34-45 doi:10.1017/S0040298213001666

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on horatiu radulescu’s fifthstring quartet (‘before theuniverse was born’) op. 89

William Dougherty

Abstract: Horatiu Radulescu’s Fifth String Quartet, ‘before the uni-verse was born’, is a shining example of his radical compositionalapproach. With an intense interest in creating a rich, numinoussound-world constructed firmly on principles of nature, scienceand ancient philosophy, Radulescu developed a unique composition-al language that breaks with traditional musical conventions. Inhopes of illuminating the inner workings behind his often enigmaticcompositional process, this article examines various aspects relatingto Radulescu’s Fifth Quartet: the work’s formal construction, with afocus on its notation and overall large-scale harmonic development;the Quartet’s rhythmic devices and their link to the philosophicalunderpinnings that drive the work; the extended instrumental stringtechniques employed throughout, the sounds they achieve, and howthey are executed; and the work’s spectral pitch organisation.

Romanian composer Horatiu Radulescu embarked on his Fifth StringQuartet, ‘before the universe was born’, in Freiburg, in 1990, and he com-pleted it five years later. The work is a shining example of his radicalcompositional approach. With an intense interest in creating a rich,numinous sound world constructed firmly on principles of nature, sci-ence and ancient philosophy, Radulescu developed a unique compos-itional language that breaks with traditional musical conventions. Inhopes of illuminating the inner workings behind his often enigmaticcompositional process, this article examines five aspects relatingto Radulescu’s Fifth String Quartet: 1) the motivation behindRadulescu’s continual return to the traditional instrumental form ofthe string quartet; 2) the Fifth Quartet’s formal construction, with afocus on the work’s notation and overall large-scale harmonic devel-opment; 3) the Quartet’s rhythmic devices and their link to the philo-sophical underpinnings that drive the work; 4) the extendedinstrumental string techniques employed throughout, the soundsthey achieve, and how they are executed; and 5) the work’s spectralpitch organisation.

Radulescu wrote six string quartets, spanning the years from 1968(when, at the age of 26, he wrote his First String Quartet Introito,Ricercare, Suonare) to 1992 (when, at age 50, he completed his SixthString Quartet, ‘practicing eternity’). Radulescu regarded his stringquartets as having a particularly high importance in his artistic output.

Tempo 68 (268) 34–45 © 2014 Cambridge University Pressdoi:10.1017/S0040298213001666


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His interest in this traditional instrumental form goes against his usualpursuit of radical instrumentations, heard in pieces like IncandescentSerene, for 12 quartets of French horn, viola, octobass flute and doublebass, or Outer Time, for 23 flutes or 14 bass flutes and 14 sound icons.To explain his continued return to the string quartet form we mustlook to Radulescu’s well-documented appreciation for Western histor-ical tradition. In an interview in 1996 he stated, ‘I have to say not onlydo I adore the Western tradition but I also think that spectrality is aglobal way of including also Byzantine and Indian music’.1 Whilehis interest in the string quartet may lie firmly in his admiration of his-torical precedent, it may also have to do with the practical implicationsassociated with the genre. As a self-proclaimed spectral composer,Radulescu continually experimented with scordatura tunings, naturalharmonics and microtonal inflections that stem from the harmonicspectrum. His spectral approach also leads to a constant explorationof colourful instrumental textures achieved by an innovative approachto playing technique; with strings, he was able to focus on the vastworld of textures associated with alternating various bow pressures,positions and speeds.

As musical notation software evolved, Radulescu began to useFinale in the early 1990s. With a somewhat limited knowledge ofengraving software, he chose to hand-write his Fifth Quartet. Thisis most likely because engraving the work with a program likeFinale would be highly impractical – formatting, in a score that straysfar from traditional notation practices, would be a nightmare forsomeone with minimal technical experience. Rather than using a trad-itional five-line staff, Radulescu employed tablature notation, denotingwhere on the strings the performers play. When he wanted an openstring, he placed an open circle on the line representing one of thefour strings. To indicate a natural harmonic, he placed a small staffwith the sounding pitch on the string to be played, accompanied bya number corresponding to the partial number. Each of the 29pages of the score is divided into four 15-second segments, addingup to one minute. The duration of each event is determined by exact-ly where each note lies in relation to the time indication at the top ofeach page. An upside-down ‘L’ symbol indicates where a note shouldstop, and a tie symbol indicates when a note should be held. The workincludes a number of string techniques of Radulescu’s own invention –a number of them developed in earlier works – for which he had hisown accompanying symbol nomenclature. In terms of dynamicsRadulescu strays from the traditional forte, piano, and so on, and ratherchooses to focus on bow pressure in combination with bow speed. Heindicates high pressure, or premuto, with an encircled upside-down tri-angle, normal pressure with an encircled ‘N,’ and light pressure orflautando with an encircled ‘F’. The position of the bow is indicatedsimilarly, with boxed letters. While the exact meaning of these abbre-viations is not specified in the performance notes of the Fifth StringQuartet, they are defined clearly in the performance notes to an earl-ier work, Das Andere, from 1984. In Das Andere, Radulescu defines ‘SP’as sul ponte (on the bridge), ‘VP’ indicates verso il ponte (near thebridge), ‘N’ indicates normal, ‘pT’ indicates un poco sul tasto (slightlyon the fingerboard), ‘mT’ indicates molto sul tasto (more on the finger-board), and ‘MT’ indicates moltissimo sul tasto (high up on the

1 Bob Gilmore, ‘“Wild Ocean”: an interview with Horatiu Radulescu’, in Contemporary MusicReview 22/1–2 (2003), pp. 105–22, here p. 120.

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fingerboard, that is, almost in the middle while using an open string,and if not, very near the left hand fingering). A line with arrowheadspointing outward on both ends indicates a very fast bow speed while aline with arrowheads pointing inward on both ends indicates a veryslow bow speed. This non-traditional approach to dynamics, bowspeed, position and pressure forces performers to think differentlythan they do when playing conventional music, ensuring a fresh inter-pretation that is free of many preconceived parameters of traditionalplaying technique. At the bottom left-hand corner of each page,Radulescu indicates a pitch spectrum on which that page’s pitch con-tent is centred (this will be discussed in more depth later). Yet whenexamining Radulescu’s notational method in the Fifth Quartet it isinteresting to note his surprising inconsistency in notational precision.While he often asks the performer to play specific natural harmonicsin the extremely high register – at one point requiring the 32nd har-monic on the cello – he also permits a great deal of freedom, withtechniques that ask players to perform, for example, ‘two very highbut simultaneous melodies on natural harmonics’. Whether this isan intentional juxtaposition of freedom and control embedded withinthe notation to provoke thoughtful consideration of performance prac-tice as a whole, or just simply a lack of clarity deriving fromRadulescu’s assumptions about players’ previous experience with hisown music, is uncertain. Either way, these questions raise a numberof interesting issues that performers must tackle when deciding to per-form the Fifth Quartet.

With this overview of Radulescu’s notational approach in mind, Iturn now to the work’s overall large-scale harmonic development.As previously discussed, each page’s pitch content is based on a spec-trum, which is indicated at the bottom left-hand corner of the page.By examining these indications, a summary of the work’s harmonicdevelopment can be made (Figure 1).

Based on the work’s scordatura Radulescu utilised six main spectralareas: C, G, D, A, E, and B. In addition to these areas, he also employsother spectra, notated by a star-like figure with two asterisks inside it.When pages contain mainly non-pitched textural sounds or vary wide-ly in pitch content, for example a large glissando, Radulescu omits aspectrum indication (noted in Figure 1 as ‘N/A’). It is interesting tonote that every single page differs in its spectral pitch content. Notonce does Radulescu remain in one defined harmonic area for overa minute. This suggests that his sense of harmonic pacing correspondsclosely to the passing of one minute.2 It is also notable that Radulescumoves almost exclusively from one harmonic area to the next (frompage to page) in fourths, fifths, and seconds.3 This focus on motionthat seems for the most part to avoid thirds and sixths is telling ofRadulescu’s approach to harmonic development. One may postulatethat his choice of harmonic motion stems from a desire for similaritiesin spectral pitch content from one minute to the next. There is a greatdeal of overlap in spectra based on a fundamental a fourth or fifthapart, due to the nature of the harmonic series, but very little overlapin those a third or sixth apart (see Figure 2). Harmonic spectra on fun-damentals a second apart have a surprising amount of pitch similar-ities above the seventh harmonic as well.

2 As mentioned above, each page corresponds to one minute of time.3 Exceptions: he moves by a third, G to B, between page 21 and 22, and by a sixth, C to A,on page 10.


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One area that we have yet to examine in terms of formal constructionis rhythm. As Radulescu’s innovative approach to rhythm in the FifthQuartet is closely tied to the literary and philosophical underpinningsthat drive the work, one must first briefly explore these referencesand their significance. As a man who constantly sought ‘. . .to be asclose to the sound as possible, to the secret deep structure of sound’4,Radulescu drew from widely diverse cultural and historical sources,‘. . .almost creating a new language by placing in the same meltingpot English, German, Latin, Italian, French and Rumanian for the titlesof his pieces, [conversing] across time with Pythagoras, Mircea Eliade,Shakespeare, and Lao Tzu’.5 In his Fifth Quartet, Radulescu uses textstaken from the Tao Te Ching, an ancient work written by Chinese phil-osopher Lao Tzu in approximately 6 BCE.6 The poetry of Lao Tzu par-ticularly interested Radulescu, as he not only found it mysticallyevocative, but also forward-thinking in terms of scientific thought.This serves as the perfect complement to Radulescu’s exacting scientificapproach to spectral pitch content and his more free-thinking, other-worldly, spiritual aims. ‘I’m very impressed by Lao-Tzu, very much,by the Taoist eighty-one poems. But if you read Lao-Tzu, “being andnon-being create each other”, it’s nearly modern physics, matter andanti-matter, you see. It’s a fantastic intuition he had’.7 Using StephenMitchell’s English translation of the Tao Te Ching, Radulescu attemptsto combine three philosophical areas in performance: writing, symbolicimage, magic; rhythm, phonetic spectrum, sound; and meaning, notion-al communication, idea and thought (Figure 3).8

Radulescu wanted a deep unity – a synthesis between the writtentext, its philosophical meaning, and the rhythm generated from articu-lating the text phonetically – that would transport the performer into aspecial state of awareness. To achieve this effect in more practical terms,he placed fragments from Mitchell’s English translation of the Tao TeChing at the top of each page of the score. The natural phonetic rhythmof these text fragments determines the rhythm of the passage belowthem, sometimes precisely and sometimes more impressionistically.When the symbol of a vertical line enclosed in a box is indicated, theplayers execute the phonetic rhythm of the text above in synch withthe other players with the same symbol, while when the symbol of a(forward) slash enclosed in a box is indicated, the players execute thephonetic rhythm of the text above out of synch with the other players.While this aspect of performance is admittedly not entirely clear fromRadulescu’s performance notes, an explicit example on page 13 of thescore allows one to see his intent clearly (Figure 4). In this example,Radulescu actually notates the rhythm of the text – six quavers dividedinto two groups of three. This corresponds to the phonetic rhythm ofthe text directly above, ‘love the world as your self’. When looking at

Figure 1:Overall harmonic development inRadulescu’s Fifth String Quartet

4 Gilmore, ‘“Wild Ocean”’, p. 107.5 Franck Mallet, in Gilmore, ‘“Wild Ocean”’, p. 108.6 The Tao Te Ching serves as the basis of philosophical Taoism.7 Gilmore, ‘“Wild Ocean”’, pp. 121–2.8 Stephen Mitchell, Tao Te Ching: a new English version (New York: Harper & Row, 1988).Radulescu used phrases from the Mitchell translation as titles for his second, third, fourth,fifth and sixth piano sonatas, as well as the fifth and sixth string quartets.

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the positioning of the text at the top of each page in relation to themusical figures below, occasionally there is ambiguity as to whichmusical figures correspond to which texts. This leads one to speculateabout the reasoning behind this level of notational imprecision. It isclear that Radulescu believed in a new sense of freedom brought onby the modern age. He sought to bring this freedom into his compos-ing, while drawing connections to natural phenomena and in a similarway to the great artists and musicians of the past.

You have to work in this sense today with new means. To create a big fresco, aLeonardo in sound. Maybe more crazy, like nature is. Like the ocean. What wesee today – it’s sometimes more crazy. From the plane, when you see thewhole ocean and whole clouds. Leonardo only imagined this. In this senseyou have more freedom also.9

Figure 2:Pitch relations (2 cents or less)between harmonic series a fifth,fourth, and major third apart

9 Gilmore, ‘“Wild Ocean”’, p. 107.


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With this insight into Radulescu’s theoretical views on freedom, wecan make some informed suppositions about his decision to leavesome ambiguity in his rhythmic notation.

Radulescu’s ingenuity extended well beyond his use of rhythm andnotation. In fact, it can be argued that his discovery and use of newextended string techniques was among the most pioneering aspectsof his music. In Das Andere, from 1984, Radulescu developed a num-ber of extended string techniques that constantly reappear in his worksover the course of the next two-and-a-half decades. In order to discussthe string techniques in the Fifth Quartet, the sounds they achieve,and how they are executed, one must look to both the performancenotes accompanying Das Andere and Radulescu’s recorded insightsinto these new playing methods. In an interview in 2006, Radulescuspoke in detail about these techniques, starting with string multipho-nics. ‘Exceptionally I use a multiphonic sound on the C string, a veryspecial technique of bowing and fingering producing a multiple“broken” sound’.10 In the notes to Das Andere, Radulescu writes thatthe multiphonic should be produced by ‘fingering a natural harmonicon the slightly lower augmented 5th or a natural harmonic on theminor 10th (intervals from the open string), bowing in a very stablepoint of contact’. As both the minor tenth fingering and the slightlylowered augmented fifth fingerings fall in between two natural har-monics, they will produce two tones when lightly touched andbowed at a slow speed with high pressure, creating a multiphonic.

Another technique that Radulescu described when speaking aboutDas Andere is the ‘u du ’u du’ technique, one that he first used in hislubiri in 1981. ‘I use a special type of phase-shifting bowing (whichRohan de Saram called ‘u du ’u du’). The bow glides very swiftlyover the string and seems to be rebounding off two imaginary walls’.11

Figure 3:From performance notes from thescore of Radulescu’s Fifth StringQuartet. © Lucero Print, used bypermission

10 ‘Intimate Rituals: works for viola’. Haratiu Radulescu in conversation with BobGilmore, Amsterdam, January 2006. Transcript online at http://www.horatiuradulescu.com/interview.html (accessed June 5 2013).

11 ‘Intimate Rituals: works for viola’.

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In the performance notes to the Fifth Quartet, he also indicates flau-tando bow pressure and a fast bow speed. In the performance notesto Das Andere, Radulescu writes at length about the technique, sayingthat the bow must alternate between VT, verso il ponte (near thebridge) and mT, molto sul tasto (more on the fingerboard). He con-tinues, making it quite clear how to perform the technique and thedesired resultant sound:

This bowing technique requires a stiffly locked arm. The bow glides swiftlyover the surface of the string changing direction very abruptly and unpredict-ably like the instantaneous movements of Noh Theatre.12 We perceive four dif-ferent pieces of information at the same time: the fundamental sound (mostaudible on open string), ‘breathing noise’ of bow hair against the string causedby the fast flautando bowing, rich variation of the harmonic content due toirregular point of contact changes of the bow. NB: point of contact must notvary during up bow and down bow, but instead in between bow changes,and the sudden change of bow mutes the previous vibration creating an uneven‘panting’-like rhythm.

Another extended technique used throughout the Fifth Quartet isknown as ‘little devils’. As Radulescu describes this technique, ‘playingharmonics with one finger . . . produces an irregular melody of veryhigh harmonics, with fast bowing, interspersed with occasional soundsof the open string, like Morse signals’.13 In the notes to the Quartet,Radulescu indicates that the ‘little devils’ are produced by playing avery high melody on natural harmonics via an unstable natural

Figure 4:Explicit rhythmic gestures inRadulescu, Fifth String Quartet,p. 13. © Lucero Print, used bypermission

12 Here we can see, once again, Radulescu drawing inspiration from widely diverse culturesand sources. ‘. . . I’m very fond of some Japanese temple music and so on – and alsoChinese and Korean and Vietnamese music and Balinese. Also African music. But weshould not integrate them in music as a gadget, in the way that was in vogue even inthe ’60s by Stockhausen and other people. . . . I think with this very global language ofthe spectrum, you can be somehow close to some tendencies in those musics . . .’Gilmore, ‘“Wild Ocean”’ p. 108.

13 ‘Intimate Rituals: works for viola’.


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harmonic played with one finger in the capo tasto – the low region ofthe string – alternating with intermittent, ‘Morse-like’ signals of theopen string. Radulescu writes that the irregular melody should be pro-duced by ‘caressing a small part of the string. . . at the bottom of thefingerboard. . . like a ’. For more guidance in the morenuanced aspects on how to perform this technique and the desiredresultant sound, he comments:

The activity of the left hand is quite refined and difficultly noticeable by anobserver, and has no relation to trills or tremolo. The harmonics all have abright and metallic sound on account of the fast bowing and +/−VP. NB Inorder to achieve the highest harmonics in the lowest fingering position ofcapo tasto more bow pressure should be applied at an extreme sul pontepoint. The whole technique resembles a cloudy phenomenon with very highregister eruptions like sparklings.

It is interesting to note here that Radulescu was aware the activity ofthe left hand would be difficult for an observer to appreciate. As thetechnique itself is not so difficult, he may have been striving to subvertobservers’ expectations. Radulescu was very concerned with the audi-ence’s perception, especially when it came to veiling his sound sourceswith a sort of mystique. In an interview about his piano concerto, TheQuest, he spoke about concealing the origin of a sound to enhance thelistening experience. ‘God doesn’t say exactly from which type ofmolecules he makes the beautiful colours of a cloud. I feel we shoulddo the same: conceal cause and effect, in order to obtain a fantasticphenomenon, which would be as beautiful as possible. It’s like aninvasion of beauty. I think it’s a type of joy, of special joy. It can bea mystic joy’.14

Briefly looking at the final three extended techniques thatRadulescu employs in the Fifth Quartet, we turn first to the high dou-ble stops on natural harmonics. In the performance notes for theQuartet, Radulescu describes this as ‘two very high but simultaneousmelodies of natural harmonics (in between the 6th and 20th over-tones; see patterns used in Das Andere)’. With the score of DasAndere as a reference, one can observe exactly what Radulescu wasreferring to in this direction.

The Σ modules of biphony are to be performed as very irregular melodiesresembling Alp-horns. When dynamically very loud, the ‘colliding’ pitch ofthe double stops produce different sounds. Their very irregular periodicshape should never use periodic rhythm or glissandi. Play always legatissimo(changing the bow unobtrusively).

Together with these instructions, Radulescu inserts a diagram thatshows the desired melodic patterns (reproduced as Figure 5). It isinteresting to note that, for the most part, one of the strings remainson the same natural harmonic while the other moves in the desiredmelodic pattern. The melodic pattern is clearly aperiodic andirregular.

Another technique Radulescu makes use of is an arpeggio figure. Inthe notes to the Quartet Radulescu writes that this technique shouldconsists of ‘arpeggios of open strings varying all parameters of thebowing and using very aperiodical micro rhythm (quasi-Baroquemicro-agogic fluctuation, i.e. minute and irregularly different valuesfor each pitch) and molto / sempre lasciar vibrare’. While most ofthis description is quite clear, ‘quasi-Baroque micro-agogic fluctuation’seems a bit convoluted. Agogic accents are brought about by

14 Gilmore, ‘“Wild Ocean”’, p. 121.

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elongating a note or delaying its onset rather than applying a louderdynamic, as in typical accents.15 In the arpeggio figures, Radulescuwanted irregular elongations or offsets of pitches to create a veryfree and aperiodic quality. As the typical arpeggio is very regularand even, Radulescu seems to be ensuring with his comment on‘quasi-Baroque micro-agogic fluctuation’ that he will achieve amuch more disjointed quality.

The final extended technique to be considered here is describedby Radulescu as ‘high natural harmonics in lasciare vibrare (unstableand slow melody) in irregular alternating with the open string’.While this description is somewhat vague, one can immediatelysee similarities between this technique and others already described.In fact, this technique is similar to the ‘little devils’ technique withhigh natural harmonics. The only difference is, in this example, thetechnique is performed with no indication of playing position, whilethe ‘little devils’ must be performed by touching natural harmonicsin the lower region of the string (near the bridge). It can be assumedfrom this that one must play, with this technique, near the head-piece. Surprisingly, this creates an entirely different quality ofsound. As opposed to the ‘little devils’, high natural harmonicsplayed near the headpiece are naturally more ‘airy’ and lesspiercing.

With an understanding of the Fifth String Quartet’s formal struc-ture, rhythm and extended string techniques, one can now lookat the true foundation of Radulescu’s compositional language: hisspectral technique. As the founder of spectralism, Radulescu basedhis harmonic vocabulary on the overtones of the harmonic series.16

Over his lifetime, he developed a number of spectral techniquesthat allowed him to develop the harmonic material in his works.Before analysing his techniques of pitch manipulation in the FifthQuartet, we must first look at the string scordatura he devised. Inmany of his works for strings, Radulescu requires the performers totune their instruments in a spectral scordatura. In this case, he doesso to allow the open strings to serve as partials of certain harmonicspectra (Figure 6).

For example, the slightly flat G♯ on the third string of violin I is thefifth harmonic in a spectrum based on the low E fundamental. At thesame time, this pitch serves as the fifteenth harmonic of a spectrumbased on low A (the lowest A on an 88-key piano). As described

Figure 5:Graphic representation ofdouble-stop technique with highnatural harmonics, from the notes tothe score of Radulescu’s Das Andere.© Lucero Print, used by permission

15 Agogic accents were important to Baroque performance practice, especially on keyboardinstruments like the harpsichord and organ where the velocity and pressure of the attackdoes not affect the sound.

16 Radulescu often claimed, controversially, that his Credo from 1969 for nine cellos was thefirst spectral work written.


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earlier, Radulescu’s Fifth Quartet is centred on the spectra of C, G, D,A, E, and B. Each of the strings in the scordatura corresponds with par-tials of these fundamentals.17 This ingenious use of open strings tocorrespond with partials of the work’s pitch centres allowsRadulescu to use the full, natural, and resonant sound quality ofopen strings at many times throughout the work. It also allows himto implement his quasi-mystical, spectrally based idea of the ‘eman-ation of the immanence’. This idea, as described in his article ‘Brainand Sound Resonance’, is where one plays the natural harmonics ofa partial, treating the original partial as a fundamental itself.18

‘Other harmonic spectra are, as it were, “immanent” within the par-tials of a single spectrum’.19 As each open string itself serves as a par-tial of one of the six fundamental pitch spectra (C, G, D, A, E, and B),playing natural harmonics on any of these strings fulfils Radulescu’sidea of the ‘emanation of the immanence’. Following the scordaturapage of the performance notes, Radulescu inserts two pages witheach string of the 16 strings of the quartet on multiple staves. Hethen calculates the partials above each open string, drawing linesbetween identical partials naturally occurring in more than one string.This very precise pre-compositional diagram shows an intense atten-tion to pitch detail. With the partials of each string listed and theirshared content, Radulescu could readily reference harmonic numbersthroughout the work, knowing that certain partials on certain stringswould correspond directly with others on other strings. It is importantto note that Radulescu occasionally draws lines between pitches that are1–5 cents different in pitch, illustrating his acceptance of a small level ofimperfection in tuning – an amount that is barely perceptible. In a num-ber of the strings, Radulescu lists pitches in the extremely high partials,some of which would be next to impossible to produce accurately with

Figure 6:Spectral scordatura in Radulescu’sFifth String Quartet. © Lucero Print,used by permission

17 See Radulescu’s indication below each string in Figure 6 as to which strings correspond towhich harmonic numbers.

18 Horatiu Radulescu, ‘Brain and Sound Resonance: The World of Self-Generative Functionsas a Basis of the Spectral Language of Music’, Annals of the New York Academy of Sciences,999 (2003), 322–63.

19 Bob Gilmore, ‘Spectral Techniques in Horatiu Radulescu’s Second Piano Sonata’, Tempo,vol. 64, no. 252 (2010), 66–78, here p. 72 fn.15.

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the flesh of a finger. Knowing this, Radulescu’s desire to notate thesepitches must stem from his extended string techniques which requirethe performers to play very ‘high melodies’ on natural harmonics. Bynotating these extremely high partials in his pre-compositional diagram,Radulescu could determine the overall pitch content of these extendedtechniques.

Turning to the spectral techniques of the Fifth Quartet, we mustfirst look at Radulescu’s use of sum and difference tones to constructchords. Sum and difference tones are psychoacoustic phenomenaachieved when two tones are played simultaneously, producing inthe listener’s ear a perceived, but not actually acoustically present,third tone. As Bob Gilmore points out, this acoustic principle is an‘idea [that] is derived from the electronic music of the 1960s and’70s, where experiments with a ring modulator showed that, undercertain conditions, the combination of two or more musical tonesyields additional ‘sum’ and ‘difference’ tones in the ear of thelistener’.20 In practical terms, if one were to produce a sine tone of1500 Hz and a sine tone of 2000 Hz, a perceived difference tone of500 Hz would typically result. Radulescu applied this principle tochord construction in a number of his works, believing that it ‘demon-strated something meaningful about harmonic relationships betweentones’.21 Replacing frequency numbers with partial numbers hebrought these principles into practice. For example, according to theprinciples of sum and difference tones, he would ‘generate’ a thir-teenth partial from the combination of the fifth partial and eighth par-tial (5 + 8 = 13). From this, he would construct a chord out of thefifth, eighth and thirteenth partials. Radulescu clearly uses this tech-nique in the sixteenth minute of the Fifth Quartet (Figure 7). In thebottom left-hand corner of the page, next to the D harmonic spectralindication, Radulescu writes ‘21, 13, 8, 5’. These numbers correspondto the partial numbers above a D fundamental and are related to eachother through the principle of sum and difference tones (5 + 8 = 13;8 + 13 = 21). In the first 15 seconds of this page Radulescu createsthis chord by stacking an open F♯ on the first string of violin I (partial5), an open D on the third string of the viola (partial 8), an A♯ aquarter-tone sharper on the fourth string of the cello (partial 13)and a G slightly flat on the fourth string of violin II. On close inspec-tion, one can see that Radulescu notates each pitch and partial numberin relation to the D fundamental next to each note.

In the second chord on this same page, Radulescu uses his ‘TaaroaChord’. The Taaroa Chord, which originates from Taaroa (1969),Radulescu’s graduation piece from the Bucharest Academy of Music,appears in a number of his later pieces, including the Second PianoSonata. The chord appears in different guises and voicings fromwork to work, suggesting, perhaps that the Taaora Chord is not onedistinct chord, but rather, a chord principle. Bob Gilmore points outthat in the Second Piano Sonata, the Taaroa Chord consists of an E,C, and F which correspond to the harmonics 5, 16, and 21 of a lowC.22 This fits clearly with Radulescu’s use of sum and differencetones (5 + 16 = 21). During the sixteenth minute of the FifthQuartet, Radulescu writes at the bottom left-hand corner of the page‘G ¼ ♯ Taaroa Chord 15, 17, 32, 48’, clearly indicating a variation on

20 Gilmore, ‘Spectral Techniques in Horatiu Radulescu’s Second Piano Sonata’, p. 70.21 Gilmore, ‘Spectral Techniques in Horatiu Radulescu’s Second Piano Sonata’, p. 70.22 Gilmore, ‘Spectral Techniques in Horatiu Radulescu’s Second Piano Sonata’, p. 71.


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the Taaroa principle, but retaining both the sum and difference concept(15 + 17 = 32) and the clash of what would conventionally be consid-ered consonant and dissonant intervals within the chord. With thisbrief look at Radulescu’s spectral scordatura, the idea of ‘emanationof the immanence’, the implementation of sum and difference tones,and the Taarora Chord, one can more fully appreciate Radulescu’sinnovative approaches to pitch organisation in his Fifth String Quartet.

The Fifth String Quartet is a wonderful example of Radulescu’scompositional approach – a unique blend of science, nature, ancientphilosophy and mysticism. With some knowledge of the work’sformal construction, rhythm, extended string techniques and pitchcontent, one can grasp the evocative juxtaposition of both freedomand control and ambiguity and precision in the music of Radulescu.While some sceptics may view his mystical side as a throwbackto the sixties, the deeper one looks into the complex inner workingsof Radulescu’s creational processes, the more revolutionary he seems.As eloquently put by clarinettist Roger Heaton, ‘[Radulescu’s] workoffers an alternative to the regression and conservatism of the neoro-mantics, the often impenetrable complexities of the post-integral seri-alists, and the mindlessness of much minimalism – a refreshinglydifferent music which is both “musical” and new’.23

A supplementary image for this article can be found online at journals.cambridge.org/TEM.

Figure 7:Radulescu, Fifth String Quartet,p. 16. © Lucero Print, used bypermission

23 Roger Heaton, ‘Horatiu Radulescu: Sound Plasma’. Contact, 26/1 (1983), p. 24.

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